Always have to simp for my boi Alexander Marcus when it comes to German artists, here are three of my favs:
https://www.youtube.com/watch?v=oiwuS-_cVYs - Soldaten der Liebe
https://www.youtube.com/watch?v=SPERjzzf_wc - Elektriker
https://www.youtube.com/watch?v=HUPES26vdDI - Disco la Cola
Adam angst (german punk rock), russkaja (from austria, based on ska and partly russian folk rythms etc. afaik), grausame töchter is also quite interesting (i can see how you wouldnt like that at all tbf). I think russkaja may be quite well known outside the borders?
Most german bands i know and listen to are already known outside of germany.
Maybe also some rap bands, that are supposedly quite good and have interesting texts (not sure about these, i listen nearly only to metal): KIZ, Alligatoah (really mainstreamy i think), maybe 257ers
I'll think about this a bit more, but thats what came to my mind rn..
Edit: ASP is amazing too, but as with russkaja, there may be quite well known abroad already?
Edit2: not really sure about most genres, as i said, i mostly listen to metal, but most german metal bands are quite well known already i think
Edit3: saltatio mortis!